If you'd like to visit state park in Austin, the McKinney Falls State Park would be your closest choice.
The closest state park to Austin proper. Just south of town. Really fun and kid/dog-friendly. There are inexpensive camping sites. The admission is $6/adult (free for kids 12 and under). Lots of leisurely hiking to be had.
5.6 miles. Every local knows it for its swimming hole, but the only state park in Austin’s borders is also a hiker's dream. The three-trail system lets you choose your own adventure. History buffs will enjoy taking the Homestead Trail, which takes you to the ruins of namesake Thomas McKinney’s stone…
“Mount Bonnell has the best view of the city. You can also park at the bottom of the park and hike to the top.”
“The pink-granite building is the centerpiece of downtown Austin, perched on a hill at 12th Street and Congress Avenue. Free guided tours are held daily, starting in the South Foyer, but brochures are also available on the first floor for self-guided tours. The Texas Legislature meets every two years, so you’ll have to check the schedule if you want to see an actual session in progress.”
“A wonderful spring-fed lagoon to sun and swim and watch people. An iconic Austin Oasis, right in the midst of the city.”
“Oh, and there's a tower of junk. The Cathedral of Junk is a monstrosity made from metal pipes, rusty wheels and clocks. And people visit it all the time. ”
“Texas is rich with history and culture. The Bob Bullock Texas Museum has done a great job capturing and depicting significant, meaningful events that contributed to the Lone Star States past present and future.”